Finite Group Databasebeta

← C3×#10619775 #14518214

Subgroups — C3×#10619775 #14518214

Order 1944.

548 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66368C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊(C3⋊D3)C311yesmaximal, characteristic, complemented
3C3×(C3⋊D3)⋊A4—31nomaximal
4#10619775C313yesmaximal, direct product factor
5C3×#4175—41nomaximal
6C22×C34C2×C311yescharacteristic, complemented
7C2×C3×C3⋊(C3⋊D3)—31no—
8C2×C3×C3⋊(C3⋊D3)—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
10C3×#1094—21no—
11#66368—23no—
12#66368C2×C313yescomplemented
13C3×AΣL(1,𝔽27)—41noSylow
14C22×C3⋊(C3⋊D3)C3211yescharacteristic, complemented
15C22×C3×C3⋊D3—31no—
16C22×C3×C3⋊D3—91no—
17C22×C3×C3⋊D3—93no—
18C3×D3×A4—91no—
19(C3⋊D3)⋊A4—33no—
20C2×C34—31no—
21C3×C3⋊(C3⋊D3)—31no—
22C3×C3⋊(C3⋊D3)A411yescharacteristic, complemented
23C3×(C3⋊D3)⋊C3—121no—
24#4175—43no—
25C22×C33—21no—
26C22×C33—33no—
27C22×C33—31no—
28C22×C33—61no—
29C22×C33—63no—
30C22×C33C3×D311yescharacteristic
31C22×C33C2×C3211yescharacteristic, complemented
32C2×C3⋊(C3⋊D3)—31no—
33C2×C3⋊(C3⋊D3)—31no—
34C2×C3×C3⋊D3—91no—
35C2×C3×C3⋊D3—93no—
36C2×C3×C3⋊D3—99no—
37C2×C3×C3⋊D3—93no—
38C2×C3×C3⋊D3—99no—
39C2×C3×C3⋊D3—91no—
40C32×A4—31no—
41C22⋊H(3,𝔽3)—61no—
42C22⋊H(3,𝔽3)C3×D313yescomplemented
43#1094—23no—
44#1094—62no—
45C3×C22⋊C9—61no—
46C34C2×A411yescharacteristic, complemented
47C3×3−1+2—81no—
48C3×H(3,𝔽3)—41no—
49AΣL(1,𝔽27)—43no—
50AΣL(1,𝔽27)—83no—
51C22×C3⋊D3—31no—
52C22×C3⋊D3—91no—
53C22×C3⋊D3—93no—
54C22×C3×D3—91no—
55C22×C3×D3—271no—
56C22×C3×D3—273no—
57C2×C3×A4—271no—
58D3×A4—93no—
59C2×C33—31no—
60C2×C33—39no—
61C2×C33—33no—
62C2×C33—31no—
63C2×C33—61no—
64C2×C33—63no—
65C2×C33—69no—
66C3⋊(C3⋊D3)—31no—
67C3⋊(C3⋊D3)C3×A411yescharacteristic, complemented
68C3×C3⋊D3—31no—
69C3×C3⋊D3—91no—
70C3×C3⋊D3—99no—
71C3×C3⋊D3—93no—
72C3×C3⋊D3—91no—
73C3×C3⋊D3—93no—
74C32×D3—361no—
75(C3⋊D3)⋊C3—123no—
76C22×C32—21no—
77C22×C32—31no—
78C22×C32—33no—
79C22×C32—31no—
80C22×C32—33no—
81C22×C32—63no—
82C22×C32—61no—
83C22×C32—66no—
84C22×C32—63no—
85C22×C32—63no—
86C22×C32—61no—
87C22×C32(C3⋊D3)⋊C311yescharacteristic
88C22×C32C32×D311yescharacteristic
89C2×C3⋊D3—91no—
90C2×C3⋊D3—93no—
91C2×C3⋊D3—99no—
92C2×C3⋊D3—99no—
93C2×C3⋊D3—93no—
94C2×C3⋊D3—91no—
95C2×C3×D3—271no—
96C2×C3×D3—273no—
97C2×C3×D3—279no—
98C2×C3×D3—279no—
99C2×C3×D3—273no—
100C2×C3×D3—271no—
101C3×A4—33no—
102C3×A4—91no—
103C3×A4—181no—
104C22⋊C9—63no—
105C33—21no—
106C33—33no—
107C33—31no—
108C33—61no—
109C33—63no—
110C33—121no—
111C33D3×A411yescharacteristic
112C33C2×C3×A411yescharacteristic, complemented
1133−1+2—83no—
1143−1+2—242no—
115H(3,𝔽3)—43no—
116H(3,𝔽3)—241no—
117C3×C9—241no—
118C23×C3—271no—
119C22×D3—91no—
120C22×D3—271no—
121C22×D3—273no—
122C2×A4—273no—
123C2×C32—39no—
124C2×C32—33no—
125C2×C32—31no—
126C2×C32—39no—
127C2×C32—33no—
128C2×C32—31no—
129C2×C32—61no—
130C2×C32—63no—
131C2×C32—69no—
132C2×C32—69no—
133C2×C32—69no—
134C2×C32—618no—
135C2×C32—63no—
136C2×C32—1081no—
137C3⋊D3—31no—
138C3⋊D3—91no—
139C3⋊D3—99no—
140C3⋊D3—93no—
141C3⋊D3—91no—
142C3⋊D3—93no—
143C3×D3—91no—
144C3×D3—271no—
145C3×D3—273no—
146C3×D3—279no—
147C3×D3—273no—
148C3×D3—271no—
149C3×D3—363no—
150C22×C3—21no—
151C22×C3—33no—
152C22×C3—31no—
153C22×C3—61no—
154C22×C3—63no—
155C22×C3—811no—
156C22×C3—811no—
157C22×C3#417511yescharacteristic, complemented
158C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
159C2×D3—271no—
160C2×D3—273no—
161C2×D3—279no—
162C2×D3—273no—
163C2×D3—279no—
164C2×D3—271no—
165A4—93no—
166C32—21no—
167C32—33no—
168C32—31no—
169C32—33no—
170C32—31no—
171C32—61no—
172C32—63no—
173C32—63no—
174C32—63no—
175C32—66no—
176C32—61no—
177C32—123no—
178C32—361no—
179C32—721no—
180C32(C3⋊D3)⋊A411yescharacteristic
181C32C3×D3×A411yescharacteristic
182C9—243no—
183C23—271noSylow
184C2×C3—39no—
185C2×C3—33no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—61no—
189C2×C3—63no—
190C2×C3—69no—
191C2×C3—271no—
192C2×C3—811no—
193C2×C3—1083no—
194D3—91no—
195D3—271no—
196D3—273no—
197D3—279no—
198D3—273no—
199D3—271no—
200C22—811no—
201C22—811no—
202C22C3×#417511yescharacteristic, complemented
203C3—21no—
204C3—33no—
205C3—31no—
206C3—61no—
207C3—63no—
208C3—363no—
209C3#1061977511yescharacteristic, direct product factor
210C3C3×(C3⋊D3)⋊A411yescharacteristic
211C2—31no—
212C2—271no—
213C2—811no—
subgroupG/H
center, hypercenterC3#10619775
commutator, cosocle, hypocenterC22×C33C2×C32
FrattiniC32C3×D3×A4
FittingC22×C34C2×C3
socleC22×C32(C3⋊D3)⋊C3
LCSG ▷ C22×C33
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#66368C2semidirect
2. C22×C3×C3⋊(C3⋊D3)C3semidirect
4. #10619775C3direct (N × H)
6. C22×C34C2×C3semidirect
9. C3×C22⋊H(3,𝔽3)D3semidirect
12. #66368C2×C3semidirect
14. C22×C3⋊(C3⋊D3)C32semidirect
22. C3×C3⋊(C3⋊D3)A4semidirect
31. C22×C33C2×C32semidirect
42. C22⋊H(3,𝔽3)C3×D3semidirect
46. C34C2×A4semidirect
67. C3⋊(C3⋊D3)C3×A4semidirect
112. C33C2×C3×A4semidirect
157. C22×C3#4175semidirect
202. C22C3×#4175semidirect
209. C3#10619775direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#663682
C22×C3×C3⋊(C3⋊D3)3
C3×(C3⋊D3)⋊A43
#106197753
C3×#41754